Hi Brian,
As far as I know you cannot deploy a DHCP server in Azure VNets:
Can I deploy a DHCP server in a VNet?
Azure VNets provide DHCP service and DNS to VMs and client/server DHCP (source port UDP/68, destination port UDP/67) not supported in a VNet. You cannot deploy your own DHCP service to receive and provide unicast/broadcast client/server DHCP traffic for endpoints inside a VNet. You can deploy a DHCP server on a VM with the intent to receive unicast DHCP relay (source port UDP/67, destination port UDP/67) DHCP traffic. A possible scenario is configuring DHCP relay from devices on-premises to an Azure VM running a DHCP server. Customer is responsible for configuring on-premise devices (for example, router configuration) to create this DHCP relay traffic to the VM's IP in Azure.
I believe this answer would answer for vMX as well.
Can I reserve a private IP address for a VM that I will create at a later time?
No. You cannot reserve a private IP address. If a private IP address is available, it is assigned to a VM or role instance by the DHCP server. The VM may or may not be the one that you want the private IP address assigned to. You can, however, change the private IP address of an already created VM, to any available private IP address.
What are the different types of IP addresses I can assign to VMs?
If this is helpful please accept answer.